Without knowing exactly what you are doing with your network config, I can take a guess and say that your router needs to re-broadcast the DNS server information it's being assigned when it gets its DHCP info from your ISP, and pass this down to clients (aka your Mac) when it assigns them their NAT addresses.

In other words, there should be a configuration option in the router's setup which should allow you to have it assign DNS addresses to client Macs and PCs.

An even better way to remedy this would be to enter a few DNS servers manually into the TCP/IP tab of the Network panel in System Preferences.